What we’ve done in this question is take each number we are given in terms of the different heights of students and subtracted each of them by the mean. Then we square this number. Again, these numbers are known as squared differences. We’ll add all the squared differences together and then divide it by how many different numbers there are in our population of data.

We’ve got 10 different heights, so the squared differences that we’ve summed up will be divided by 10. Lastly, we’ll take the square root of the number to find the final standard deviation of the population.

What we’re doing here is we’re making use of the idea that the variance is just the standard deviation squared. So if we take the unsimplified version from question 1, we can square the square root, which removes the square root. We then find that the variance equals 153.1.

How to calculate sample standard deviation

Asides from finding the population standard deviation, you can take a sample from the population and find the sample standard deviation. Its calculation is similar to finding the population standard deviation but the denominator is different. We’ll be using this formula instead: